Risk-adjusted discount rates and capital budgeting under uncertainty

This paper is concerned with the valuation of multiperiod cash flows in a world where prices are determined according to the Sharpe-Lintner-Black model of capital market equilibrium. We find that the current market value of any future net cash flow is the current expected value of the flow discounted at risk-adjusted discount rates for each of the periods until the flow is realized. The discount rates are known and non-stochastic, but the rates for the different periods preceding the realization of a cash flow need not to be the same, and the rates relevant for a given period can differ across cash flows. The risk adjustments in the discount rates arise because of uncertainties about reassessments through time of the expected value of a flow and the relationships between these reassessments and the corresponding reassessments of the expected cash flows of all firms.     

An axiomatic approach to the valuation of cash flows

We model a stream of cash flows as an optional stochastic process, and value the cash flows by using a continuous and strictly positive linear functional. By applying a representation theorem from the general theory of stochastic processes we are able to study this valuation principle, as well as properties of the stochastic discount factor it implies. This approach to valuation is useful in the non-presence of a financial market, as is often the case when valuing cash flows arising from insurance contracts and in the application of real options.     

Valuation in Emerging Markets: A Simulation Approach

Most of the foundations of valuation theory have been designed for use in developed markets. Because of the greater, and in some cases different, risks associated with emerging markets (although recent experience might suggest otherwise), investors and corporate managers are often uncomfortable using traditional methods. The typical way of capturing emerging-market risks is to increase the discount rate in the standard valuation model. But, as the authors argue, such adjustments have the effect of undermining some of the basic assumptions of the CAPM-based discounted cash flow model. The standard theory of capital budgeting suggests that estimates of unconditional expected cash flows should be discounted at CAPM discount rates (or betas) that reflect only “systematic,” or “nondiversifiable,” market-wide risks. In practice, however, analysts tend to take what are really estimates of “conditional” expected cash flows—that is, conditional on the firm or its country avoiding a crisis—and discount them at higher rates that reflect not only systematic risks, but diversifiable risks that typically involve a higher probability of crisis-driven costs of default. But there is almost no basis in theory for the size of the increases in discount rates. In this article, the authors propose that analysts in emerging markets avoid this discount rate problem by using simulation techniques to capture emerging-market risks in their estimates of unconditional expected cash flows—in other words, estimates that directly incorporate the possibility of an emerging-market crisis and its consequences. Having produced such estimates, analysts can then discount them using the standard Global CAPM.     

Valuation of Internet Stocks—An IPO Perspective

We empirically investigate valuations of Internet firms at various stages of the initial public offering (IPO) from two perspectives. First, we examine the association between the valuation of Internet IPOs and a set of financial and nonfinancial variables, which prior anecdotal or empirical evidence suggests may serve as value drivers. Second, we document differences in IPO valuations between Internet and non-Internet firms as well as across different stages in the IPO process—i.e., initial prospectus price, final offer price, and first trading day price—within each set of firms. Our primary two conclusions are as follows. First, there are noticeable differences between valuations of Internet and non-Internet firms, especially at the prospectus and final IPO stage. Specifically, the valuation of non-Internet firms generally follows the conventional wisdom regarding valuation: positive earnings and cash flows are priced, while negative earnings and negative cash flows are not. The valuation of Internet firms, however, departs from conventional wisdom, with earnings not being priced, and negative cash flows being priced perhaps because they are viewed as investments. This difference between the two classes of firms may be expected, given the age and unique nature of the Internet industry. Second, there are significant differences between the initial valuation of firms at the prospectus and IPO stage and their valuation by the stock market at the end of the first trading day. For non-Internet firms, the difference is largely ascribed to the relative offering size. For Internet firms, however, the differences are with respect to positive cash flows, sales growth, R&D, and high-risk warnings, in addition to the relative offering size.     

Valuing and pricing IPOs

This paper investigates how underwriters set the IPO firm’s fair value, an ex-ante estimate of the market value, using a unique dataset of 228 reports from French underwriters. These reports are issued before the IPO shares start trading on the stock market and detail how underwriters determined fair value. We document that underwriters often employ multiples valuation, dividend discount models and discounted cash flow (DCF) analysis to determine fair value but that all of these valuation methods suffer from a positive bias with respect to equilibrium market value. We also analyze how this fair value estimate is subsequently used as a basis for IPO pricing. We report that underwriters deliberately discount the fair value estimate when setting the preliminary offer price. Part of the intentional price discount can be recovered by higher price updates. We find that, controlling for other factors such as investor demand, part of underpricing stems from this intentional price discount.     

What Do FAS 157 “Fair Values” Really Measure: Value Or Risk?

FAS 157, the U.S. accounting standard that prescribes how fair values of assets and liabilities are to be measured when other U.S. GAAP standards require fair valuation, stipulates that fair values be measured as the exit values of assets and liabilities—the proceeds for assets hypothetically sold on the date of the financial report, and, correspondingly, the amount required to settle liabilities on the date of the financial report. This conceptual article argues that exit values do not reflect the value of the net assets of the firm to shareholders, which is best reflected by discounted cash flows to maturity. Moreover, exit values—biasing fair values downward when markets are illiquid—have a pernicious, systemic risk effect; specifically, they give rise to write‐downs that in turn cause contagion: prices of equities and other financial instruments of peers react negatively, leading to further write‐downs by those peers. This may have aggravated the recent financial crisis. However, while exit values are not proper measures of value to shareholders, they are useful measures of downside risk when prospects turn sour for a firm. Thus, both exit values and discounted cash flows should be presented in financial statements.     

Two Different Ways of Treating Corporate Cash in FCF Valuations—and the Importance of Getting the Cost of Capital Right

The methods for calculating free cash flow presented in texts on financial statement analysis and valuation appear to be very different from those in corporate finance texts, causing some confusion among academics as well as practitioners. Financial statement analysis and valuation texts generally begin by valuing just the enterprise operations—that is, the entity that engages in the firm's primary revenue‐generating activities—and then adding back the value of its cash holdings and other financial assets. The corporate finance approach is typically to value all the assets together, including financial assets that are not used in the production of the goods and services provided by the firm. Using a simple example, the authors show that the valuation of the equity ownership of the firm should be the same for both methods of calculating free cash flow, provided the analyst makes the appropriate adjustments to the method for calculating the cost of capital (WACC) used to discount forecasted free cash flows to a present value.     

Why Is Long‐Horizon Equity Less Risky? A Duration‐Based Explanation of the Value Premium

We propose a dynamic risk‐based model that captures the value premium. Firms are modeled as long‐lived assets distinguished by the timing of cash flows. The stochastic discount factor is specified so that shocks to aggregate dividends are priced, but shocks to the discount rate are not. The model implies that growth firms covary more with the discount rate than do value firms, which covary more with cash flows. When calibrated to explain aggregate stock market behavior, the model accounts for the observed value premium, the high Sharpe ratios on value firms, and the poor performance of the CAPM.     

The Role of Real Options in Capital Budgeting: Theory and Practice1

Most discussions of capital budgeting take for granted that discounted cash flow (DCF) and real options valuation (ROV) are very different methods that are meant to be applied in different circumstances. Such discussions also typically assume that DCF is “easy” and ROV is “hard”—or at least dauntingly unfamiliar—and that, mainly for this reason, managers often use DCF and rarely ROV. This paper argues that all three assumptions are wrong or at least seriously misleading. DCF and ROV both assign a present value to risky future cash flows. DCF entails discounting expected future cash flows at the expected return on an asset of comparable risk. ROV uses “risk‐neutral” valuation, which means computing expected cash flows based on “risk‐neutral” probabilities and discounting these flows at the risk‐free rate. Using a series of single‐period examples, the author demonstrates that both methods, when done correctly, should provide the same answer. Moreover, in most ROV applications—those where there is no forward price or “replicating portfolio” of traded assets—a “preliminary” DCF valuation is required to perform the risk‐neutral valuation. So why use ROV at all? In cases where project risk and the discount rates are expected to change over time, the risk‐neutral ROV approach will be easier to implement than DCF (since adjusting cash flow probabilities is more straightforward than adjusting discount rates). The author uses multi‐period examples to illustrate further both the simplicity of ROV and the strong assumptions required for a typical DCF valuation. But the simplicity that results from discounting with risk‐free rates is not the only benefit of using ROV instead of—or together with—traditional DCF. The use of formal ROV techniques may also encourage managers to think more broadly about the flexibility that is (or can be) built into future business decisions, and thus to choose from a different set of possible investments. To the extent that managers who use ROV have effectively adopted a different business model, there is a real and important difference between the two valuation techniques. Consistent with this possibility, much of the evidence from both surveys and academic studies of managerial behavior and market pricing suggests that managers and investors implicitly take account of real options when making investment decisions.     

The impact of opacity on bank valuation during the global financial crisis: A channel analysis

Prior literature suggests that opacity in the banking industry is mainly caused by a lack of informativeness in the assessment of the quality of bank assets. Examining a sample of bank holding companies in the United States, we find that there is a negative relationship between opacity and bank valuation during the 2007–2009 global financial crisis. We further attempt to identify two potential channels through which opacity negatively affects bank valuation during the financial crisis: a cash flow channel and an expected return channel. We show that one channel flows from bank profitability, measured by return on equity and return on assets, confirming a cash flow channel, whereas an expected return channel, proxied by the implied cost of capital, only works for small banks. Overall, this study sheds light on the relationship between in-transparency and bank value discount during a global recession.     

On the Matter of Parity among Financial Obligations

The lessons of the leasing literature concerning the impact of leases on the debt capacity of a firm are reviewed and summarized to establish an approach to the analysis of the corporate bond refunding decision. A general proposition regarding financial obligation parity is established, and from that a clear bond refunding decision rule is developed. Previous debates in the literature about appropriate discount rates and about the appropriate cash flows to be discounted for refunding decisions are clarified.     

A Reconsideration of Tax Shield Valuation

A quarter‐century ago, Miles and Ezzell (1980) solved the valuation problem of a firm that follows a constant leverage ratio L = D/S. However, to this day, the proper discounting of free cash flows and the computation of WACC are often misunderstood by scholars and practitioners alike. For example, it is common for textbooks and fairness opinions to discount free cash flows at WACC with beta input β _S = [1 + (1 ? τ)L]β_u, although the latter is not consistent with the assumption of constant leverage. This confusion extends to the valuation of tax shields and the proper implementation of adjusted present value procedures. In this paper, we derive a general result on the value of tax shields, obtain the correct value of tax shields for perpetuities, and state the correct valuation formulas for arbitrary cash flows under a constant leverage financial policy.     

A Synthesis of Equity Valuation Techniques and the Terminal Value Calculation for the Dividend Discount Model

This paper lays out alternative equity valuation models that involve forecasting for finite periods and shows how they are related to each other. It contrasts dividend discounting models, discounted cash flow models, and residual income models based on accrual accounting. It shows that some models that are apparently different yield the same valuation. It gives the general form of the terminal value calculation in these models and shows how this calculation serves to correct errors in the model. It also shows that all models can be interpreted as providing a particular specification of the terminal value for the dividend discount model. In so doing it shows how one calculates the terminal value for the dividend discount formula. The calculation involves weighting forecasted stocks and flows of value with weights determined by a parameter that can be discovered from pro forma analysis.     

How Do Investment Banks Value Initial Public Offerings (IPOs)?

Abstract:  We investigate the valuation and the pricing of initial public offerings (IPOs) by investment banks for a unique dataset of 49 IPOs on Euronext Brussels in the 1993–2001 period. We find that for each IPO several valuation methods are used, of which Discounted Free Cash Flow (DFCF) is the most popular. The offer price is mainly based on DFCF valuation, to which a discount is applied. Our results suggest that DDM tends to underestimate value, while DFCF produces unbiased value estimates. When using multiples, investment banks rely mostly on future earnings and cash flows. Multiples based on post-IPO forecasted earnings and cash flows result in more accurate valuations.     

From dividend yield to discounted cash flow: a history of UK and US equity valuation techniques

This article explores how, as capital markets developed, equity valuation methods changed. The history of equity valuation is described, from its early origins during the South Sea Bubble, through the new issue boom of the nineteenth century and the stock market booms of the 1920s and 1950s. The moves from dividend yield and asset backing, to earnings yield and then P/E ratios are chronicled. The article compares developments in the UK and the US, in particular the relative slowness of the UK market to adopt US-pioneered techniques such as the P/E ratio, the concept of value versus growth stocks, and using intrinsic value to determine whether shares are cheap or dear. The article concludes with a discussion of the relatively slow introduction of the dividend discount model and of discounted cash flow as equity valuation tools on both sides of the Atlantic.     

Managerial discretion to delay the recognition of goodwill impairment: The role of enforcement

Under International Financial Reporting Standards, managers can use two approaches to increase the estimated fair value of goodwill in order to justify not recognizing impairment: (1) make overly optimistic valuation assumptions, and (2) increase future cash flow forecasts by inflating current cash flows. Because enforcement constrains the use of optimistic valuation assumptions, we hypothesize that enforcement influences the relative use of these two choices. We test this hypothesis by comparing a sample of 1,958 firms from 36 countries that are likely to delay recognizing goodwill impairment (suspect firms) to a sample of control firms. First, we find that firms in high‐enforcement countries use a higher discount rate to test goodwill for impairment than firms in low‐enforcement countries. We also find a more positive association between discount rate and upward cash flow management for suspect firms than for control firms. This result is consistent with suspect firms substituting optimistic valuation assumptions with inflated current cash flows. Second, we find that, relative to control firms, suspect firms exhibit higher upward cash flow management in high‐enforcement countries than in low‐enforcement countries. Third, we show that suspect firms in high‐enforcement countries are more likely to eventually impair goodwill.     

Valuation of Corporate Innovation and the Pricing of Risk in the Biopharmaceutical Industry: The Case of Gilead

Much of a firm's market value derives from expected future growth value rather than from the value of current operations or assets in place. Pharmaceutical companies are good examples of firms where much market value comes from expectations about drugs still in the development “pipeline.” Using a new osteoporosis drug being developed by Gilead Sciences, Inc., the author combines discounted cash flow methods values and real option models to value it. Alone, discounted cash flow (DCF) calculations are vulnerable to the assumptions of growth, cost of capital, and cash flows. But by integrating the real options approach with the DCF technique, one can value a new product in the highly regulated, risky and research‐intensive Biopharmaceutical industry. This article shows how to value a Biopharmaceutical product, tracked from discovery to market launch in a step‐by‐step manner. Improving over early real option models, this framework explicitly captures competition, speed of innovation, risk, financing need, the size of the market potential in valuing corporate innovation using a firm‐specific measure of risk and the industry‐wide value of growth operating cash flows. This framework shows how the risk of corporate innovation, which is not fully captured by the standard valuation models, is priced into the value of a firm's growth opportunity. The DCF approach permits top‐down estimation of the size of the industry‐wide growth opportunity that competing firms must race to capture, while the contingency‐claims technique allows bottom‐up incorporation of the firm's successful R&D investment and the timing of introduction of the new product to market. It also specifically prices the risk of innovation by modeling its two components: the consumer validation of technology and the expert validation of technology. Overall, it estimates the value contribution per share of a new product for the firm.     

Estimating cost of capital in firm valuations with arithmetic or geometric mean – or better use the Cooper estimator?

We test the extent and determinants of bias effects of the arithmetic as well as the geometric mean estimator and the estimator of Cooper [1996. Arithmetic versus geometric mean estimators: Setting discount rates for capital budgeting. European Financial Management 2 (July): 157–67] regarding discount rate estimation for firm valuation by way of a bootstrap approach for 13 different countries. The Cooper estimator is superior to both the geometric and the (conventional) arithmetic mean estimator. However, a ‘truncated’ version of the arithmetic mean estimator leads generally to better estimation outcomes than the Cooper estimator. This means that, in order to reduce problems of upward-biased firm value estimates, expected cash flows beyond a certain time horizon are completely neglected in terminal value estimation. Such an approach seems particularly reasonable for the valuation of young growth companies as well as for companies from quickly developing countries such as Brazil, China, or Thailand, because the bias in terminal value estimation is increasing in the growth rate of future expected cash flows.     

The Valuation of Cash Flow Forecasts: An Empirical Analysis

This article compares the market value of highly leveraged transactions (HLTs) to the discounted value of their corresponding cash flow forecasts. For our sample of 51 HLTs completed between 1983 and 1989, the valuations of discounted cash flow forecasts are within 10 percent, on average, of the market values of the completed transactions. Our valuations perform at least as well as valuation methods using comparable companies and transactions. We also invert our analysis by estimating the risk premia implied by transaction values and forecast cash flows, and relating those risk premia to firm and industry betas, firm size, and firm book-to-market ratios.